Thanks Gang,
I was thinking of (1) as well at the time of the post but neglected to mention it. The others are kind of extensions of that.
To clarify, I was wondering if there was ever a reason to have something like this [1 -3 -1 1 3], an arbitrary contrast that sets some values positive, others negative, and they do not sum to zero. This is more the kind of thing that puzzled me. Why would someone do that? Or would they? I think the implication of your answer is that non-zero sum GLTs are basically used for tests where all terms are positive and unitary. That right?
cheers
Iain